Keywords

1 Introduction

There are many situations wherein the activity of driving requires drivers to interact with each other via a car system. This activity includes merging and overtaking on a highway, or giving way at an intersection or a narrow road. It is possible to perform the interactions even when drivers cannot see each other. To ensure a smooth flow of traffic, drivers determine their own driving behaviors using external information, such as the environmental relationship between themselves, other cars and traffic norms, which are systematically or empirically accumulated. For instance, the environmental relationship could include such things as relative distance and relative speed between two cars, and the traffic norms that include right of way and traffic signs.

Previous studies on the interactional behavior between drivers have mainly examined the principle that a driver makes a decision based on the kind of external information they receive. For instance, Hiramatsu, Jang, Naemoto, Ito, Yamazaki, & Sunda (2017) predicted driving behaviors based on the relative distance between a car and the preceding car when following a car in front [1]. They concluded that people’s driving behaviors could be predicted by referring to the relative distance between the two cars when two cars are driving in convoy.

Additionally, it has been shown that people’s driving behaviors characteristics can be estimated by the relative speed and distance to the car in front, and the model could predict what drivers would do next based on this estimation [2].

However, some studies argue that consideration of other cars affects the decision of the driving behaviors in interactive scenarios between several drivers, such as following a car in front or merging [3]. Yoshikawa & Takagi (2008) examined what factors affect driving behaviors by analyzing what participants said when driving with a talk aloud protocol. Consequently, the utterances about the behaviors of other cars and the decision-making based on the behaviors accounted for about 40% of the total utterances. For instance, it included a report that “I decided to decelerate in consideration of the oncoming car because the road is narrow.” Thus, it is suggested that the driving behaviors is determined based on not only objectively external information, but also an estimation of the driving tendency and intentions of the other driver involved.

In psychology, humans can estimate mental states of another people that cannot be directly observed from the outside (hereinafter, “the Model of Others”; e.g., purpose, intention, and belief) to determine their own behaviors. Such mental functions are called Theory of Mind [4]. Simulation Theory has been proposed as one of the mechanisms for estimating the Model of Others [5]. According to Simulation Theory, humans simulate what they would do if they were in another person’s situation and convert their own state of mind to that of the other person’s state of mind. Then, they would estimate the Model of Others by assuming that the other’s mental state is the same as their own and make decisions based on considering this.

In this study, a merging scenario on a highway was used as an experimental situation. Specifically, in order to achieve merging while considering the other car in the adjacent lane, participants decide to accelerate so as to come out ahead of the other car (hereinafter, “Lead decision”), or decelerate to join the lane behind the other car (hereinafter, “Follow decision”). In such a situation, participants need to estimate the Model of the Others and consider the state of the other driver and make a decision based on their simulation. They might think “If I were the driver of the other car, would I lead or follow in this situation?” and make a Lead/Follow decision based on their estimated answer. If decisions are made in this way, the Lead/Follow decision in the merging lane is determined according to their assumption of Lead/Follow decision in the main lane, and vice versa. For instance, a driver who pulled out in front of the other car in the main lane when merging would follow the other car when merging from the merging lane.

If the driver decides their own behaviors based on the simulation that “If I were a driver of the other car, would I lead in front of or follow behind the car for merging in this situation?,” their decisions in the merging lane are dependent on the assumed behaviors in the main lane.

2 Method

In this experiment, we used a highway merging junction as an experimental task and examined how drivers make lane-change decisions when moving from the merging lane to the main lane. This experiment was performed with the approval of the research ethics committee at the Institute of Innovation for Future Society (MIRAI) of Nagoya University (approval number: 2019–17).

2.1 Participants

Twenty-four participants (13 women and 11 men, mean age 43.92, range 22–60, SD = 11.40) were paid $50 for the 90-min experiment.

2.2 Task

Participants drove in a merging scenario on the highway that consisted of two lanes; a main lane and a merging lane (see Fig. 1). On the highway, two cars were adjacent to one another: a car driven by participants (hereinafter, “self car”), and a car driven in the adjacent lane to the self car (hereinafter, “other car”). Until the car reached 360 m from the starting point, a wall separated the lanes so that participants could not see the other car in the adjacent lane. During this period, participants were required to keep driving at 80 km/h.

Fig. 1.
figure 1

The task situation. Participants drive a car on a road consisting of two lanes, the main lane and the merging lane. On the road, there are two cars: a car driven by participants; and an autonomous car driven on the adjacent lane to the road the self car is being driven on.

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Participants drove in the following two conditions; they drove the self car in the merging lane and merged the self car into the main lane (hereinafter, “merging lane condition”), and drove the self car in the main lane and let the other car merge from the merging lane into main lane (hereinafter, “main lane condition”). At that time, participants made Lead/Follow decisions.

This experiment was performed using a driving simulator (see Fig. 2). As shown in Fig. 2-a, the road created by Unity (ver.2019.2.17) was projected on five screens (three in front and one on each side). Participants sat in the driver’s seat set in front of the screen and drove in the same way as driving an actual car (see Fig. 2-b).

Fig. 2.
figure 2

The experimental environment using a driving simulator.

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2.3 Procedure

Participants drove under the following two conditions: 5 times in the practice trial, and 25 times in the actual trial. In the actual trial, when participants completed a lane-change, whether the self car lead in front of or follow behind the other car was recorded as a data point. The order of the trials was counterbalanced among participants.

  • The merging lane condition:

Participants drove a car in the merging lane and then merged into the main lane. Participants then decided whether to lead in front of (Lead) or follow behind the other car (Follow decision). The other car was set to run autonomously at a constant speed.

  • The main lane condition:

Participants drove a car in the main lane and decided whether to lead in front of (Lead) or follow behind the other car coming from the merging lane (Follow decision). The other car ran at a constant speed and merged smoothly into the main lane only when there was a certain amount of distance between the two cars.

Five levels of relative distances were set between the self car and the other car. Specifically, when the self car reached 300 m (shortly before the 360 m mark where other car could be observed), the other car was located +10 m, +5 m, 0 m, −5 m, or −10 m from the 300 m mark. Participants performed five trials under each relative distance for a total of 25 trials. The order of the 25 trials was randomized.

3 Results

3.1 Overall Result

To understand the overall tendency of how decisions are made in the main lane and the merging lane, we conducted logistic regression analysis to predict lead probability at the relative distance (−10 m, −5 m, 0 m, +5 m, +10 m). Figure 2 shows the results of this analysis.

The lead probability at the intercept of the model (in short, the lead probability when the relative distance is 0) was calculated. The results show that the lead probability when driving in the main lane was 22% higher than when driving in the merging lane (the probability of a leading decision in the main lane condition = .68, and the probability of a leading decision in the merging lane condition = .46) (Fig. 3).

Fig. 3.
figure 3

Logistic regression models to predict lead probability with relative distance in each lane.

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3.2 Result of Individual Behaviors

The following analysis was conducted to verify whether participants determined their own driving behaviors according to the Model of Others based on Simulation Theory. We used logistic regression analysis to calculate the probability that the self car would lead in front of the other car when participants drove in each lane based on the relative distance (−10 m, −5 m, 0 m, +5 m, +10 m). We defined the intercept of the regression equation when the relative distance was 0 as the “probability of making a leading decision.” Figure 4 shows the relationship of the probability of making a leading decision.

Fig. 4.
figure 4

Correlations for the probability of making a leading decision between the main lane and merging lane conditions. The vertical axis indicates the probability that the self car would lead in front of the other car in the main lane condition. The horizontal axis indicates the probability that the self car would lead in front of the other car in the merging lane condition.

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If participants estimated the Model of the Others through use of Simulation Theory and decided their own actions based on the estimated model, the following result is predicted: when participants drive in the merging lane, the Model of the Others is estimated based on their main lane driving behaviors. In this case, if the participant tends to follow the other car in the main lane, they presume that the other car in the main lane will also follow the other car. Therefore, the participant would pull out in front of the other car. The participants who displayed this behavior are plotted in the fourth quadrant (lower right) in Fig. 4. Conversely, the participants who tended to pull out in front of the other car in the main lane would tend to follow the other car in the merging lane; such participants are plotted in the second quadrant (upper left) in Fig. 4. In short, if the participants make merging decisions using the Model of the Others based on Simulation Theory, their decisions should be plotted in the second and fourth quadrants.

Consequently, ten participants (45% of the total) were plotted in the first quadrant (upper right), eight (30%) were plotted in the second quadrant (upper left), and six (25%) were plotted in the third quadrant (lower left). No participants were plotted in the fourth quadrant (lower right). The participants in the first quadrant (upper right) tended to lead in front of the other car from both lanes. The participants in the third quadrant (lower left) tended to follow the other car from both lanes. The participants in the second quadrant (upper left) tended to lead in front of the other car from the main lane and follow it from the merging lane.

However, the second (upper left) and fourth (lower right) quadrants, where participants who use the Model of Others would be plotted, there were participants plotted only in the second quadrant. There may be reasons other than that the decision being made using the Model of Others. Considering that the participants with low lead probabilities in the merging lane and with high Lead probabilities in the main lane are plotted in the second quadrant, it is possible that the participants in the second quadrant made the merging decision based on the Japanese traffic norm, “the car running in the main lane should be given priority over the one running in the merging lane” [6].

These results did not support our hypothesis that drivers make merging decisions using the Model of the Others based on Simulation Theory. Rather, these findings might support that drivers make decisions based on either innate driving tendencies or traffic norms that indicate that the main lane is the priority lane.

4 General Discussion

In this study, we examined how drivers make Lead/Follow decisions on the highway in two situations. The first is the situation that the driver’s car merges from the merging lane to the main lane. The second is the situation that the driver’s car runs in the main lane, and the other car merges from the merging lane to the main lane. As a result, it was shown that the driver would drive according to their own driving tendency or traffic norms. This suggests that Simulation Theory proposed in the Theory of Mind is unlikely to be used in decision-making while merging from one lane to another.

It is assumed that participants thought that other drivers do not always make the same inference as they might make. Simulation Theory assumes that the self and the other make the same inference to estimate the Model of Others [7]. Therefore, if a driver deems the other driver not to be identical as him- or herself, the driver would be unlikely to estimate the mental status of the other driver based on simulation. This leads to the following question; do drivers make merging decisions mechanically on their own driving habits or traffic norms?

Regarding the estimation of the Model of Others, apart from Simulation Theory, “Theory Theory” has been proposed [8]. According to Theory Theory, humans estimate the Model of Others by interpreting behaviors a person took in a situation according to the individual’s knowledge, such as stereotypes. Humans can estimate the Model of Others of an opponent based on the impression formed by the opponent’s behaviors even in a scenario where it is their first interaction with the opponent [9, 10].

It is also possible that the drivers form and use impressions toward the driver of the other car during driving. Hosokawa, Shino, Kamata, Kanamori, Fuwamoto, & Umemura (2008) propose a mathematical model that estimates the driving tendency of the driver based on driving behaviors, such as the degree of deceleration and the timing of indicating his or her intention using blinkers [11]. For instance, this model estimates that drivers with frequent deceleration and early use of their blinkers tend to drive cautiously. In this way, the impression of the other driver is formed by collating the driver’s attribution of the other car with prior knowledge (e.g., stereotype, patterns of behaviors). The driver’s attribution is determined by his or her sex, social status, driving experience or driving tendency (e.g., the degree of acceleration/deceleration, average speed, and timing of the use of their blinkers). For instance, considering the drivers’ social status of the other car, a driver might think that luxury car drivers tend to have higher average speeds. Considering the driver’s driving tendency of the other car, a driver might think that drivers with a small relative distance between two cars when following a car tend to drive aggressively. Then, it is expected that drivers make a decision about their own driving behaviors based on their impressions. In other words, driving decisions and behaviors can be strongly influenced not only by external information but also by the impression of others.

For instance, the appearance of a particular car type may affect the impression formation toward others. Doob & Gross (1968) found that low-priced light cars tend to give a low impression of the owner’s social status, and the interaction partner’s driving behaviors would become more aggressive [12]. Yazawa (2004) investigated that the three factors, “with or without learner plate,” “high or low social status” and “driver’s gender” affect the number time participants used their horns. In that study, the car type was used to control the social status of the owner (high status: luxury car; low status: light car) [13]. Consequently, it was shown that the number instances a horn was used was significantly higher when the other car had a learner plate or was considered of low status.

The above discussion suggests that the attributes of the other car and the driver may affect driving behaviors, and investigation about the effects of these factors is an important issue to be looked into in the future.

In this study, the car’s exteriors were of the same type. Therefore, if the other car had a sports car’s exterior, participants may have a more aggressive impression toward the driver of the other car. Conversely, if the other car had a light car’s exterior, participants may have a more cautious impression toward the driver of the other car. Specifically, if the other car were a sports car, the lead probability of participants is expected to be lower than in this experiment, and if the other car had a light car, the lead probability is expected to be higher. Following on from this, it is necessary to further examine whether the driving behavior of participants is influenced by manipulating the impression of the other car and so the driver’s behavior of the other car.